Contribution to the Geometry Optimization of an Oscillating Water Column Wave Energy Converter

Energy Procedia 36 ( 2013 ) 565 – 573

1876-6102 © 2013 The Authors. Published by Elsevier Ltd.Selection and/or peer-review under responsibility of the TerraGreen Academydoi: 10.1016/j.egypro.2013.07.065

TerraGreen 13 International Conference 2013 - Advancements in Renewable Energy and Clean Environment

Contribution to the Geometry Optimization of an Oscillating Water Column Wave Energy Converter

B.BOUALIa,b*, S.LARBIb aUniversité de Lagouat-Laboratoire de génie des Procédés, Université de Laghouat-03000,ALGERIA

bEcole nationale Polytechnique-Département de génie Mécanique, Alger-16000,ALGERIA

Abstract

In this paper, we discuss the effects of geometry and dimensions of an oscillating water column energy converter chamber on the efficiency of this device. The main purpose of this study is to optimize the geometry and dimensions of the energy converter to get the maximum power available in a progressive wave with constant period and wavelength. Modeling and numerical simulation are performed by using the commercial software ANSYS- ICEMCFD & CFX. The numerical wave tank used in this model is assumed to be equipped with a Stokes second order wave generator type. The fluid flow is set to be biphasic (air/water), two-dimensional and k- turbulent model. Since the study is focused on the temporal variation of the pressure, the turbine power extraction is modeled by a vent that shape and location can be variables. The simulation results shows that the size of the chamber, the immersion depth of the front wall of the device and its orientation versus the flow direction have a very significant impact on the performance of the device. © 2013 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the TerraGreen Academy. Keywords: Wave energy converter WEC, Oscillating water column OWC, Numerical wave tank, hydrodynamique efficiency, CFD simulation

1. Introduction

The oscillating water column (OWC) concept is used for extracting power from ocean waves. An OWC comprises a collector chamber, which takes power from the waves and transfers it to the air within the chamber, and a power take off (PTO) system, which converts the pneumatic power into electricity or some other usable form. The PTO is typically an air turbine (although water pumps have been considered

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566 B. Bouali and S. Larbi / Energy Procedia 36 ( 2013 ) 565 – 573

as an alternative) and, for simplicity, the air turbine normally selected is of a self-rectifying form so that whether the collector is exhaling or inhaling, the turbine is driven in the same direction. The most commonly used form of PTO in the OWC application is the Wells turbine-induction generator combination [1], (figure 1).

The most published numerical models on this device have as main purpose to obtain better values of plant efficiency which depends, mainly, of the water free surface oscillations inside the chamber and the PTO modeling. The key parameters of interest are the front wall submergence depth a and the chamber size b normalized with respect to water depth h (figure 2) as described by Evans and Porter [2] in a theoretical analysis of an OWC device. But in practice, the nonlinear turbine modeling, the front lip shape and thickness play a significant role. Sarmento [3], in an experiment work, and Zhang et al.[4], in a numerical study, have modeled the turbine by a circular hole.

Another important problem is how to model the flow outside and inside the chamber. The linear theory considers that the flow is potential and important approximations are used to simplify the governing equations of motion [5]. Karami et al. [6] have modeled the interior oscillating water surface by a thin rigid plate, and considered a potential flow motion. Asid Zullah et al. [7] treated, using Ansys CFX commercial code, a wave energy conversion by means of a savanius rotor and have used a k-

turbulent model for flow simulation. The hydraulic power required to calculate OWC efficiency is determined by integrating, over a period

time, the product of air pressure in the chamber and the air flow rate [4], [8], [9], or by using the instantaneously product of the displacement variation of the water free surface and the air pressure in the chamber. In this case the water surface is regarded as an oscillating flat plate [6], [10].

In both experimental and numerical wave tank a wave generator (wavemaker), which can be a piston type or a flap type, is needed. The desired wave characteristics (amplitude and wavelength) depend on the stroke of the moving body. Linear wavemaker theory is described by Dean et al. [11] and, for non linear small amplitude waves, details are provided by Ursell et al. [12]. The boundary conditions on the wavemaker can be implemented either wavemaker motion or velocity induced by wavemaker paddle.

In this paper, the efficiency of an OWC wave energy converter is determined by numerical simulation with regard to some parameters of water column design, particularly the immersion depth and orientation, vs. flow direction, of the chamber front wall. ANSYS-ICEM CFD is used for geometry and meshing. ANSYS-CFX is used to model and solve the flow field equations. The obtained result data are treated with MATLAB to calculate the efficiency.

Fig. 1. Schematic of an OWC wave energy converter

Free Surfaceoscillations

Air turbine

Wave flow direction

OWC Frontwall

B. Bouali and S. Larbi / Energy Procedia 36 ( 2013 ) 565 – 573 567

2. Methodology

2.1. Geometrical and physical characteristics

In this section, we consider a rectangular chamber having, on the upper side, a rectangular vent. The front wall is immersed in water and is oriented at an arbitrary angle with respect to the direction of flow. The geometrical characteristics of the device are shown in Figure 2. Considering upstream wave amplitude and wavelength corresponding to the second-order Stokes theory, we therefore impose the velocity components provided by this theory as boundary conditions on the wavemaker. The wave characteristics are chosen so that it is well represented by Stokes second order solution. Different regions of validity for various theories are described by Le Mehaute [13]. The wave considered in this study has a constant period T, wavelength and incoming wave height H.

According to the second order theory, the equation of the free surface elevation is [5]:

)tkxcos()khcosh()kh(sinh)khcosh(H)tkxcos(H 2222

82 3

2

(1)

Where, t is the time, h the water depth, k the wave number and is the angular frequency. The horizontal component u and the vertical component w of the local fluid velocity are given by the

following relations:

)wtkx(cos)kh(sinh

)zh(kcoshkH)tkxcos()khcosh(

)hz(kcoshHgku 2216

32 4

2

(2)

)tkx(sin)kh(sinh

)zh(ksinhkH)tkxsin()khcosh(

)hz(ksinhHgkw 2216

32 4

2

(3)

The dispersion relation is given by:

)htanh(gT 22

2

(4)

The corresponding wave incident power [14] per unit width is:

64

22

6491

221

16 hkH

)khsinh(khH

TgPin (5)

Assuming that the water free surface in OWC behaves as a flat plate, the hydrodynamic power transferred to the air column inside the chamber can be determined as follows:

dtdZ

.b.pPhyd pa (6)

Where, pa is the air column pressure, b is the size of the chamber and Zp is the free surface elevation inside the chamber.

The OWC efficiency is computed by the ratio of the hydrodynamic power to the incident power:

PinPhyd (7)


Fig.2. (a) Geometrical characteristics of OWC, (b) water wave properties

Our study was focused on the OWC front wall chamber, in particular its immersion depth and orientation versus the flow direction. However, five cases are to be distinguished as shown in Fig.3. All cases are studied for a same progressive monochromatic wave that has constant height and wavelength.

Fig.3. Different possibilities to orient the front wall of the OWC chamber 2.1. Modeling

Modeling of geometry and meshing are performed by using ICEM CFD. Blocking strategy has been used to generate multi-block structured grid. Near the water free surface, around the chamber front wall and in the air column inside the chamber a fine mesh was made because the results accuracy in these key areas is very important (figure 3.a). To reduce the CPU time, we have set the domain length to three times the wavelength and cells located towards the key areas are made larger (about 32 cells per wavelength). The number of mesh cells in this situation, for each case, is about 6500.

The numerical wave tank, (as shown in Fig.3.b.) is subject to the following boundary conditions: at the upstream boundary, velocities provided by equations (2) and (3) and volume fraction for each phase are imposed. Fixed pressure (atmospheric pressure) is set at the vent and on the upper side outside the chamber. In the rest of the domain, wall with no slip condition is applied.

Bottom

(a)

h

a

b

Vent

Flow direction

H

h

y

x

(x)

Bottom

Water level at rest

(b)


ANSYS-CFX is used to solve the governing equations for two-phase flow (air / water). The solver uses finite volume method to solve Navier-Stokes equations and VOF (volume of fluid) method is used for tracking and locating the free surface (interface between phases). The water flow is set to turbulent k- model and air is assumed to be real gas at 25°C. Advection scheme is set to high resolution and transient scheme is set to second order backward Euler. The velocity boundary conditions and initial volume fractions are introduced using CFX expression language (CEL).

Fig.4. (a) Domain discretization (b) Numerical wave tank and its boundaries

3. Numerical results

Calculations in this study are performed by considering an incident wave that physical parameters satisfy the Stokes second-order theory. The period T is set to 5s, the wave height is H=1m (amplitude =0.5m) and the water depth is h=6m. According to equation (4), the wavelength is determined by using the Matlab function fsolve; we obtain approximately = 32.19m. In all transient analysis performed in the present study the time step is set to 0.01s

In first step, the five possibilities of orientation of the front wall shown in Fig. 3 are examined to determine the best configuration to be studied as a function of the immersion depth. Finally, we discuss the effect of the chamber size on the device performances.

For post processing, some variables are necessary and therefore they must be saved during analysis. The pressure in the air column and the motion of the water free surface, inside the OWC chamber, are necessary for calculating the device efficiency. The movement of the free surface is obtained by converting the hydrostatic pressure to a height of fluid column. The time derivative is then calculated by using Euler differentiation scheme.

3.1 Effect of the OWC front wall orientation

Fig.5 (a) and (b) shows the time history of the pressure variation in the air column and the displacement velocity of the free surface inside the chamber for the first classical case (1). The air pressure is measured at a point in the center of the chamber above the water surface. Hydrostatic pressure in the water is measured at a point, in the center, where the air volume fraction is zero in all times. By

(b)

(a)


using equations (5), (6) the wave and hydrodynamic powers are evaluated and the instantaneous OWC efficiency is computed according to equation (7). Fig.6 illustrates variations for this parameter. The mean value over 10 periods is 15.43% and a peak of 46.87% is reached. These values are obtained for an immersion depth a= 1m and a chamber size b=5m. In order to obtain an established and fully developed flow, the calculation is performed for about 20 wave periods. The first 10 periods are ignored to avoid the transient effects.

Fig.5. (a) time history of pressure in the air column, (b) OWC free surface oscillations for case (1)

Fig.6. OWC efficiency against time over 10 periods for case (1)

Table 1 summarizes the results obtained for different orientations of the OWC front wall. We note that the configuration (4), which is counter current orientation, is the best arrangement to maximize the device efficiency. So, we use this configuration to examine the effect of the other key parameters.

(b)

(a)


Table 1. Performances of the OWC for different orientations of the front wall with respect to the flow direction

Case Average efficiency Max efficiency

1 ( =90°) 0.1543 0.4687

2 ( =45°) 0.1528 0.5421

3 ( =-45°)

4 ( =0°)

5 ( =180°)

0.1202

0.1697

0.1517

0.4602

0.8181

0.5798

3.2 Effect of the front wall immersion depth

In this analysis we vary the immersion depth of the front wall a as a function of water depth h similarly to the study conducted by Evans and al. [2]. The OWC efficiency is calculated for several values of the ratio of the immersion depth to the water depth, especially 0.125, 0.25, 0.5, and 0.70, as shown in Fig. 7.

The maximum value obtained for the OWC efficiency is 24.53% at an immersion depth of about 0.45h. By using a cubic fitting as shown in Fig.5, the optimal value is 24.06% at an immersion depth of about 0.4h.

Fig.7. Mean efficiency against the immersion depth of the front wall

0.1 0.2 0.3 0.4 0.5 0.6-0.2

-0.1

0

0.1

0.2

Residuals

0.1 0.2 0.3 0.4 0.5 0.6-0.1

0

0.1

0.2

0.3

a/h

Effi

cien

cy

NumericalCubic fitting


3.2 Effect of the chamber size

Fig.8 shows variations of the OWC efficiency versus the chamber width b normalized to water depth h. The maximum value obtained for the OWC efficiency is 26.83% for a chamber size of about 0.92h.

By using a 4th degree polynomial fitting as shown in Fig.8, the optimal value is 25.72% for a chamber width of about 0.80h.

Fig.8. Mean efficiency against the OWC chamber size

4. Conclusion

A k- turbulent model was used to simulate a biphasic air/water flow in order to determine the hydrodynamic efficiency of an OWC wave energy converter. To be closer to reality, a Stokes second-order incident wave was considered. CFD simulations were conducted for different configuration of the device. Results reveal that orientation of the air chamber front wall in counter flow direction at a 180° angle is the best configuration regarding to the unit efficiency. The front wall immersion depth is a key parameter. The optimal value obtained in this study is situated between 0.38 and 0.44 times the water depth. The width of the OWC chamber also affects, in a remarkable manner, the performance of the device and the results of simulation shows that the best dimension is located around the water depth (between 0.8h and h). Therefore, it is reasonable to combine these conditions in a single design to increase the wave energy conversion.

In order to improve the OWC efficiency, this study is to be extended to consider the effect of the front wall thickness, wave climatology, and chamber geometries other than rectangular.

0.5 0.75 1 1.25 1.5 1.75 2-0.2

-0.1

0

0.1

0.2

Residuals

0.5 0.75 1 1.25 1.5 1.75 20.1

0.15

0.2

0.25

0.3

0.35

b/h

Effi

cien

cy

Numerical4th degree fitting


References

[1] T. V. Heath A Review of oscillating water columns, Phil. Trans. R. Soc. A 2012 370, 235-245, doi: 10.1098/rsta.2011.0164. [2] Evans DV, Porter R. Hydro dynamic characteristics of an oscillating water column device. Appl. Ocean Res. 1995; 17:155e64. [3] Sarmento A.J.N.A. Wave flume experiments on two dimensional oscillating water column wave energy devices. Experiments in Fluids 12, 286 292 (1992) [4] Zhang Y., Zou Q-P., Deborah G. Air water two-phase flow modeling of hydrodynamic performance of an oscillating water column device. Renewable Energy, Volume 41, May 2012, Pages 159-170. [5] Dean, R.G., Dalrymple, R.A. Water Wave Mechanics for Engineers and Scientists, World Scientific Publishing Company, 1991 [6] V. karami, m.J.Ketabdari, A. K. Akhtari Numerical Modeling of Oscillating Water Column Wave Energy Convertor, IJARER Vol. 1, Issue. 4, pp. 196-206, 2012 [7] M. Asid Zullah, Y-H. Lee Performance evaluation of a direct drive wave energy converter using CFD, Renewable Energy 49 (2013) 237e241. [8] G. Nunes, B. Valerio, P. Beirao, J.S.D. Costa Modeling and control of a wave energy converter, Renewable Energy 36 (2011) 1913e1921. [9] W. Sheng, T. Lewis, R. Alcorn On wave energy extraction of oscillating water column device, 4th

International Conference on Ocean Energy, 17 October, Dublin 2012. [10] Stappenbelt, B., Cooper, P. Mechanical Model of a Floating Oscillating Water Column Wave Energy Conversion Device. 2009 Annual Bulletin of the Australian Institute of High Energetic Materials, 1 34-45. 2010. [11] Robert G. Dean , Robert A. Dalrymple, Water Wave Mechanics for Engineers and Scientists, World Scientific 1991. [12] URSELL, E, R. G. DEAN, and Y. S. Yu, Forced Small Amplitude Water Waves: A Comparison of Theory and Experiment, J. Fluid Mech., Vol. 7, Pt.. 1,1960. [13] B. Le Mehaute, An introduction to hydrodynamics and water waves, Springer-Verlag, 1976.

[14] McCormick M. E. Ocean Wave Energy Conversion, Wiley-Interscience, 1981.

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Contribution to the Geometry Optimization of an Oscillating Water Column Wave Energy Converter